To evaluate the amplitudes, we make use of standard tools including
the unitarity method [1]} and the Bern-Carrasco-Johansson
(BCJ) [2]}, [3]} double copy, which gives gravity integrands
in terms of corresponding gauge-theory ones. We build on the
\(D\) -dimensional version of the unitarity method of
Ref. [4]} in order to fix the rational terms in the
amplitudes. At four points gauge-theory tree-level amplitudes
automatically satisfy the duality between color and kinematics, so the
associated double-copy relations also hold automatically on the
unitarity cuts. We use this to express the cuts of the gravity loop
integrands directly in terms of the corresponding gauge-theory ones.
By using the double copy our computation parallels the corresponding
gauge-theory one [4]} allowing us to import many of the
same steps into the gravitational amplitude calculations.
